课程名称： 统计学
课程性质： 必修
课程范围： 指数分配、抽样分配、区间估计......
开课教师： 罗光达
开课学院： 社会科学院
开课系级： 财政系
考试日期(年月日)： 2014.1.13
考试时限(Mins)： 18:30-21:30
附注：
试题本文：
Guidance:
1.Do all questions and write legibly.
2.Total point=100; Suggested=150 minutes.
3.Please keep your original copy of quizzes/midterm/final, in
case you need it to correct your scores.
4.最后答案取至小数点后第二位，但若为查表值需与附表相同。
Question 1 (10%)
Let X have a binomial distribution with parameters n=150 and p=0.6.
Approximate the probability that 82 < x < 101.
Question 2 (10%, 5/5)
假设一栋大楼无预警跳电的相隔天数服从指数分配，且过去的纪录显示平均
50天会发生2次跳电。求下列事件发生之机率：
(1) 两次无预警跳电的间隔时间少于10天。
(2) 两次无预警跳电的间隔时间多于20天。
Question 3 (10%, 5/5)
A statistical analysis of 1000 long-distance telephone calls made
from the headquarters of the Bricks and Clicks Computer Corporation
indicates that the length of these calls is normally distributed
with μ = 240 seconds and σ = 40 seconds.
(1) What is the probability that a call lasted between 110 and 180
seconds?
(2) What is the length of a particular call if only 2.5% of calls
are shorter?
Question 4 (20%, 10/10)
Let a random variable X have the following probability distribution
x -2 0 2
P(X=x) 0.2 0.6 0.2
_
(1) Obtain the sampling distribution of X for a random sample of 2.
(2) Calculate E(X) and Var(X) for the sampling distribution in (1).
Question 5 (20%)
A survey of 1000 workers were asked how much they used the Internet
at work. 600 said they used it within limits, and 260 said they did
not use the Internet at work.
(1) Construct a 95% confidence interval estimate for the proportion
of all workers who used the Internet within limits.
(2) What sample size was required under 95% confidence interval, if
you want to estimate the population proportion of within a sampling
error of all workers who used the Internet within limits ±0.02 ?
Question 6 (20%, 5/15)
The file contains the amount that a sample of 9 customers spent for lunch
($) at a fast food restaurant
4.20 5.03 5.86 6.45 7.38 7.54 8.46 8.47 9.87
_
(1) Find X and S.
(2) Construct a 95% confidence interval estimate for the population mean
amount spent for lunch($) at a fast food restaurant, assuming a normal
distribution.
Question 7 (10%)
请解释何谓分层抽样(Stratified Sampling)及部落抽样(Clustered Sampling) ?
并各举一例加以说明。